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A A "" VA RM A5I2a. SKESEARCH MEMORANDUM :i'." :, ., 4~' a. . i... .. .* ..: ... i'ii; EFFECT OF BLUNTNESS ON THE DRAG OF SPHERICALTIPPED ^: "^ / .:. : s A.. :: Ni : 'e . ..' : 1ll:: :.:. N A TRUNCATED CONES OF FINENESS RATIO 3 AT MACH NUMBERS 1.2 TO 7.4 By Simon C. Sommer and James A. Stark Ames Aeronautical Laboratory Moffett Field, Calif. UNIVERSITY OP FLORIDA DOCUMENTS N*RTMENT 120 MARSON SCIENCE LIUSARY P.O. BQX 117011 GANEVILLE, FL 326117011 USA TIONAL ADVISORY COMMITTEE FOR AERONAUTICS WASHINGTON April 25, 1952 .".: .,:; :*,:_ ..:: "' "^ ^ ^ ^ ^ ^  ^ i  * :; :, ; : *., ::. . C: r :i~tr..: ."': .. " F ', '*, [ a ":'i,,1 .9 414 .. ....=.. ...:'".. .:1 *2 ;:: i""i, '. {"'i" ..:. :"..!. . 'i i i l ; : :,.... ... ....... ... . fa: 0.: .: .i. .i : NACA RM A52B13 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS RESEARCH MEMORANDUM THE EFFECT OF BLUNTNESS ON THE DRAG OF SPHERICALTIPPED TRUNCATED CONES OF FINENESS RATIO 3 AT MACH NUMBERS 1.2 TO 7.4 By Simon C. Sommer and James A. Stark SUMMARY The drag nf spherically blunted conical models of fineness ratio 3 was investigated at Mach numbers from 1.2 to 7.4 in the Reynolds number range from 1.0 x 106 to 7.5 x 106. Results of the tests showed that slightly blunted models had less drag than cones of the same fineness ratio throughout the Mach number range. At Mach numbers less than 1.5, drag penalties due to large bluntnesses were moderate but these became severe with increasing Mach number. Wave drag obtained by the method of Munk and Crown, in which the wave drag is determined by integrating the momentum loss through the head shock wave, showed that the wave drag and total drag followed the same trends with increasing bluntness. Wave drag was also estimated by com bining the experimental wave drag of a hemisphere with the theoretical wave drag of a conical afterbody, and this estimate of wave drag is believed to be adequate for many engineering purposes. INTRODUCTION Blunt noses are being considered for some supersonic vehicles for the purpose of housing guidance equipment. In some cases a high degree of bluntness is required, and the drag penalty due to this bluntness may be significant. On the other hand, work done by others indicated that slightly blunt noses will have less drag than pointed noses of the same fineness ratio. For these two reasons the drag of bluntnose shapes is of current interest and therefore an investigation was made in the Ames supersonic freeflight wind tunnel to determine the influence of blunt ness on drag at Mach numbers from 1.2 to 7.4. The models tested were truncated cones with spherical noses having bluntness ratios of nose NACA RM A52B13 diameter to base diameter from 0 to 0.50. All models had a fineness ratio of length to base diameter of 3. SYMBOLS A frontal area of model, square feet CD total drag coefficient total drag) 1CD total drag penalty compared to the cone (CDmodel CDone) CDb base drag coefficient base drag C, q.A / CDf skinfriction drag coefficient (skinfriction drag) 1 \qA CDv total drag coefficient based on volume to the twothirds power total drag qV2/3 CD, wave drag coefficient (wave drag d diameter of the base, feet dn diameter of the nose, feet M freestream Mach number q freestream dynamic pressure, pounds per square foot R freestream Reynolds number, based on axial length of model V volume of model, cubic feet MODELS The models tested were truncated circular cones with tangentially connected spherical nose segments, as shown in figure l(a). All models had a fineness ratio of 3, with base diameters and lengths of 0.45 and 1.35 inches, respectively. The models had holes bored in their bases for aerodynamic stability. Five different shapes were tested with nose diam eters of 0, 71/2 percent, 15 percent, 30 percent, and 50 percent of the base diameter. NACA RM A52B13 The models were constructed of 75ST aluminum alloy. The maximum measured dimensional deviations were as follows: nose diameter, 0.0005 inch; base diameter, 0.0015 inch; length, 0.020 inch; and the halfangle of the conical section, 0.050. For the majority of the models tested, the deviations were less than half of those given. The machined and polished surfaces had average peak to trough roughnesses of 20 microinches. In no case was there any correlation between the scatter of the test results and the dimensional deviations of the models. TESTS AND EQUIPMENT These tests were conducted in the Ames supersonic freeflight wind tunnel (reference 1) where models are fired from guns into still air or upstream into a supersonic air stream. The models were launched from a smoothbore 20 mm gun, and were supported in the gun by plastic sabots (fig. l(b)). Separation of the model from sabot was achieved by a muzzle constriction which retarded the sabot and allowed the model to proceed in free flight through the test section of the wind tunnel. Drag coefficient was obtained by recording the timedistance history of the flight of the model with the aid of a chronograph and four shadow graph stations at 5foot intervals along the test section. From these data, deceleration was computed and converted to drag coefficient. With no air flow through the wind tunnel, Mach numbers varied from 1.2 to 4.2 depending on the model launching velocity. This condition is referred to as "air off." Reynolds number varied linearly with Mach number from 1.0 X 106 to 3.3 x 106, as shown in figure 2. With air flow established in the wind tunnel, referred to as "air on," the combined velocities of the model and Mach number 2 air stream, with the reduced speed of sound in the test section, provided test Mach numbers from 3.8 to 7.4. In this region of testing, Reynolds number was held approximately at 4 X 106 by controlling testsection static pressure. In addition, some models were tested at approximate Reynolds numbers of 3 x 106 and 7.5 x 10 at Mach number 6. The purpose of this investigation was to obtain drag data near 0 angle of attack. This report includes only the data from models which had maximum observed angles of attack of less than 30 since larger angles measurably increased the drag. Since there are no known systematic errors, the accuracy of the results is indicated by the repeatability of the data. Examination of these data shows that repeat firings of similar models under almost identical conditions of Reynolds number and Mach number yielded results for which the average deviation from the faired curve was 1 percent and the maximum deviation was 4 percent. NACA EM A52B13 RESULTS AND DISCUSSION Total Drag Variation of the total drag coefficient with Mach number for each of the models tested is presented in figure 3. No attempt was made to join the airoff and airon data due to differences in Reynolds number, recovery temperature, and stream turbulence. Variation of drag coeffi cient with Mach number for all models is similar, in that the drag coefficient continually decreased with increasing Mach number. There is, however, a tendency for the blunter models to show less decrease in drag coefficient with increasing Mach number. These data have been crossplotted in figure 4 to show the effect of bluntness on total drag coefficient for various Mach numbers. The nose bluntness for minimum drag shown by each curve decreases with increasing Mach number. This is shown by the dashed curve. At Mach number 1.2 the bluntness with minimum drag is 28 percent as compared to 11 percent at Mach number 7. At Mach numbers less than 1.5, drag penal ties for models with bluntnesses approaching 50 percent are moderate but grow large with increasing Mach number. As Mach number becomes greater than 4.5, the drag penalties for large bluntnesses do not increase meas urably but nevertheless are severe. Drag in terms of volume may be important in some design consider ations. In order to indicate the relative merit of the models in terms of drag for equal volume, the data of figure 4 have been replotted in figure 5, where drag coefficient is referred to volume to the twothirds power. These curves show that moderate and even large bluntnesses (the degree of bluntness depending on Mach number) may be used to decrease the drag for equal volume. Wave Drag The variation of the total drag with model bluntness is believed to result primarily from the variation of the wave drag of the models and to be essentially independent of the base drag and skinfriction drag. In order to show this, the wave drag of the blunt models was estimated from the experiment by assuming the combined base drag and skinfriction drag independent of bluntness and these results were compared to wave drag determined by the method of Munk and Crown (reference 2). In the estimation of the wave drag, the base drag and skinfriction drag used were those of the cone, and were obtained by subtracting the theoretical wave drag of the cone (reference 3) from the experimental total drag of the cone at each Mach number. These values of combined base drag and NACA RM A52B13 skinfriction drag were then subtracted from the total drag of the blunt models to obtain the wave drag of each model. The results are shown by the solid curves in figure 6, where wave drag is plotted as a function of model bluntness. In the method of Munk and Crown, the wave drag is computed by summing up the momentum change through the head shock wave. Since part of the wave shape is unaccounted for because of the limited field of view in the shadowgraphs, an approximation suggested by Nucci (reference 4) was used to estimate the wave drag omitted. This approximation gives the upper and lower limits of the wave drag omitted. The mean value of these limits was used in all cases. These results are indicated by the points in figure 6. The mean disagreement between the results of this method and the results obtained by assuming base drag and skinfriction drag independent of bluntness is 7 percent. Another method of estimating wave drag of the blunt models is by the addition of the wave drag of a hemisphere to that of a conical afterbody. Collected data showing the manner in which the wave drag of a hemisphere varies with Mach number is shown in figure 7.1 The wave drag of the hemi spherical tip was obtained directly from this figure, and the wave drag of the conical afterbody was obtained from the tables of reference 3. The results of this method are presented as the dashed curves in figure 6. A comparison of the results of this method with the results of the first two methods shows that although the method of estimating wave drag by the addition of the wave drag of a hemisphere to that of a conical after body appears to overestimate wave drag of the blunt models, it may nevertheless be adequate for many engineering purposes. Viscous Effects The effect of Reynolds number on total drag coefficient was investi gated at Mach number 6. In figure 3, data for three Reynolds numbers, 'Wave drag of a hemisphere at Mach numbers from 1.05 to 1.40 was esti mated from the data of reference 5 by calculating the wave drag of the pointed body and assuming that the drag due to the afterbody and fins was not a function of nose shape. At Mach numbers of 15, 2.0, 3.0, and 3.8, wave drag of a hemisphere was obtained from unpublished pres sure distributions from the Ames 1 by 3foot supersonic wind tunnel. Wave drag of a hemisphere at Mach numbers of 3.0, 4.5, 6.0, and 8.0 were estimated from total drag measurements of spheres (reference 6) by sub tracting 70 percent of the maximum possible base drag and neglecting skinfriction drag. The possible error introduced by estimating the wave drag of the pointed body of reference 5 and the base drag of the sphere is believed to be no greater than 4 percent. NACA RM A52B13 3 X 106, 4 X 106, and 7.5 x 106 are included for cones and 50percent blunt models. For the cones, the drag coefficient increased approximately 10 percent with increasing Reynolds number. For the 50percent blunt models little or no change in drag coefficient was measured. The vari. ation in drag coefficient for the cones was undoubtedly due to changes in the boundarylayer flow on the models at varying Reynolds numbers, as shown by the shadowgraphs in figure 8(a). At a Reynolds number of 3 x 106 the clearly defined wake (as indicated by the arrow in the figure) is associated with laminar flow. At high Reynolds numbers, the diffused wake indicates turbulent flow. Referring to figure 8(b), the boundarylayer wakes of the 50percent blunt models appear diffused and turbulent at all Reynolds numbers. Since the wake of the 50percent blunt model at Reynolds number of 3 X 106 appears turbulent compared to the laminar wake of the cone at this condition, it is concluded that boundarylayer transition occurred at lower Reynolds numbers on the 50percent blunt model than on the cone. An interesting flaw phenomenon is illustrated in figure 9 by shadowgraphs of two cones at Mach number 3.7. The shadowgraph in figure 9(a) shows a smooth flow condition in contrast to a nonsteady disturbed flow condition shown in figure 9(b). The disturbed flow seems to consist of regions of turbulent air moving aft on the model surface, with pressure waves attached to the leading edges of these regions. Flow disturbance of this nature was observed occasionally on cones at small angles of attack at Reynolds numbers of 2.5 X 106 and greater. Cones with angles of attack in the order of 30 to 60 consistently had disturbed flow. This flow condition occurred less often on blunt models than on cones; and when present on blunt models, was always of slight intensity. Data for models that exhibited this flow condition were not included in this paper. The effect of flow disturbance on cones with angles of attack of less than 30 was to raise the drag about 8 percent. This increase in drag is attributed to increases in base drag as well as wave drag. CONCLUSIONS From this investigation, the following conclusions were drawn for spherically blunted conical models of fineness ratio 3: 1. Small amounts of spherical bluntness (nose diameters in the order of 15 percent of base diameter) have been found to be beneficial for reducing drag. 2. For large spherical bluntnesses (nose diameters in the order of 50 percent of base diameter) drag penalties were moderate at Mach numbers of less than 1.5, but became severe with increasing Mach number. NACA RM A52B13 3. Estimation of wave drag by combining experimental values of wave drag of a hemisphere with wave drag of the conical surfaces is believed to predict wave drag adequately for many engineering purposes. Ames Aeronautical Laboratory, National Advisory Committee for Aeronautics, Moffett Field, Calif. REFERENCES 1. Seiff, Alvin, James, Carlton S., Canning, Thomas N., and Boissevain, Alfred G.: The Ames Supersonic FreeFlight Wind Tunnel. NACA RM A52A24, 1952. 2. Munk, Max M., and Crown, J. Conrad: The Head Shock Wave. Naval Ordnance Lab. Memo 9773, 1948. 3. Staff of the Computing Section, Center of Analysis, under the direc tion of Zdenek Kopal: Tables of Supersonic Flow Around Cones. M.I.T. Tech. Rep. No. 1, Cambridge, 1947. 4. Nucci, Louis M.: The ExternalShockDrag of Supersonic Inlets Having Subsonic Entrance Flow. NACA RM L50Gl4a, 1950. 5. Hart, Roger G.: Flight Investigation of the Drag of RoundNosed Bodies of Revolution at MachNumbers from 0.6 to 1.5 Using Rocket Propelled Test Vehicles. NACA RM L51E25, 1951. 6. Hodges, A. J.: The Drag Coefficient of Very High Velocity Spheres. New Mexico School of Mines, Research and Devel. Div., Socorro, New Mexico, Oct. 1949. Digitized by the Internet Archive in 2011 with funding fion University of Florida, George A. Smathers Libraries with support from LYRASIS and [he Sloan Foundation http://www.archive.org/details/effectofbluntnes00ames NACA RM A52B13 0.075 d dio. 0.15 d die. 0.30 d dia. 050d dio. d* .45 inches 3d  9.46  b Cone, 0O blunt Z1 7i % blunt I5 Z blunt 30 % blunt 50 % blunt (a) Model geometry Figure 1 Models tested. NACA RM A52B13 NACA I~ A52B13 11 4t .., a ::::::, s 2 i  III *o,.: w: >i <: m c li5 ^ s ^ * *^ co \u s suofq/w 'y "'aqwnu splouA'ay NACA BM A52B13 .50 be 1 .40.50 ^ S J30.40.50 .20.30.40.50 .10.20.30.40.50 S 0.10.20.30.40 Mach number, M Figure 3. Variation of total drog coefficient with Moch number. NACA RM A52B13 13 .5 M.3.2 .4 SR=. Ox /06 Z5 .4 I /. x .3 2.0 4 2.6x l06 8 ttti 6. O 4x /06 o 0 10 20 30 40 50 Percent bluntness, dn/d xlOO Figure 4. The effect of bluntness on totlo drag coefficient NACA RM A52B13 50 Figure 5. The effect of bluntness on total drag coefficient based on volume to the twothirds power (3 1% *s O 10 20 30 40 Percent bluntness, d,/d x 100 NACA RM A52B13 From experiment, assuming (CDob Cg ) independent of bluntness  Extropoloed to hemisphere o From experiment, method of references 2 and 4  Estimated by method of this report "V  .8 M=2 .2 n ,h l,;,.  M=3 I Mx6 /AC I47 0 20 40 6 Percent bluntness, dn/d x /00 Figure 6. Variation of wave drog coefficient with bluntness 80 100 A NACA RM A52B13 _ 4. 4. I *lb 41 tlb s 4 ae < I Z I 4* 0 _ _ At g)o /uaiJa#sin 6a0p OAOM s 44 ft. _iL1 NACA RM A52B13 R = 3 x l R = 4 x 10 R = 7.5 x 106 A16704 (a) Cones. (b) The 50percent blunt models. Figure 8. Shadowgraphs of cones and 50percent blunt models at Mach number 6. NACA RM A52B13 (a) Smooth flow. (b) Disturbed flow. Figure 9. Shadowgraphs comparing smooth flow with disturbed flow on cones at Mach number 3.7, Reynolds number of 3 x 106. NACA Langley Field, Va. ~i~R~E~~ `'sra L 0 . i aTd E &&m 5q .4 5 m1na 4 oa 0 c 0 0 a  N a 1 It0 0 U m 0 @2 =a  E a 5 Cu m @2 .. @2 2 m 8 (D w z C2 0 52 I ;i @ ;p .0 ,4; C4 .4 H C4 CO 0 SP.  0 to m 0. n z  B d"T J fSt^ 6 fl5 ^4 cj di s's 0 S '" ; m o \ a) rn 02 I 2 ) P4 .g Z z m, o 0 M El M 00 P4 m 0j Ci "O  t) ~ 000 o U0r4 Do1 a a w!. t Zana 0 E z Z ~ a Z IDa I E a c 1.o' jS 93!B)S a 3g o~~ E.~~ OaO~ z gg0s ,;g 8a^q9 ;rS* . E1 S4 0^ g ^ * V 0 I ~5 I8 I S t 4 0 w X y 0:3 10 0 0 31H 1 :15 21 . 1400 02 In~ bG O 0 e0 k 0 " w EjGoCD b 5 I0 0 a5iU0 w w 4 5 to 0 5  F4i ;N m 1 c .at 0 CO 0 S0 B C ] 1 mI. i ?~ UNIVERSITY OF I UNMWSTy DOCUMENTS 120 MARSTOy P.O. BOX 1170 GAINESVIE, I FLORIDA I . 6 5723 . FR FLORI A .'.. DER"Mr" ":'. SCIENCE UBRARY 11 32611.7011 USA ; .. . .. ... . . . 